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RUN REVIEW · Specialist Mathematics · Units 3 & 4 · Tech-free

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11 Sep 2026, 9:24 p.m.

20Serious score
01 During a one-minute revision round: A small p-value is evidence
A that the alternative has probability p This does not satisfy the stated relationship.
B that the null is certainly true This does not satisfy the stated relationship.
C of zero sampling variation This does not satisfy the stated relationship.
D against the null hypothesis It means the observed statistic is unusual under the null.

Written for icaijy.com · U3–4 · Hypothesis tests · answered at 100 ms

02 Which response best completes this VCE-style item? If position is \(\vec r(t)\), acceleration is
A \(\int\vec r(t)dt\) This does not satisfy the stated relationship.
B \(|\vec r(t)|\) This does not satisfy the stated relationship.
C \(\vec r\prime\prime(t)\) Acceleration is the second time derivative of position.
D \(\vec r\prime(t)\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Kinematics · answered at 100 ms

03 \(\cos(A-B)=\)
A \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.
B \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.
C \(\cos A-\cos B\) This does not satisfy the stated relationship.
D \(\sin A\cos B\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Trigonometry · answered at 100 ms

04 A student is checking a worked solution. Two non-zero vectors are perpendicular when their dot product is
A −1 always This does not satisfy the stated relationship.
B 1 This does not satisfy the stated relationship.
C their magnitude product This does not satisfy the stated relationship.
D 0 The dot product includes cos 90° = 0.

Written for icaijy.com · U1–2 · Vectors · answered at 100 ms

05 During a one-minute revision round: The vector from A to B is
A \(\vec b-\vec a\) Endpoint position minus start position.
B \(\vec a-\vec b\) This does not satisfy the stated relationship.
C \(\vec a+\vec b\) This does not satisfy the stated relationship.
D \(\vec a\cdot\vec b\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Vectors · answered at 100 ms

06 A student is checking a worked solution. \(\int e^{ax}\,dx=\)
A \(ae^{ax}+C\) This does not satisfy the stated relationship.
B \(\frac1a e^{ax}+C\) Differentiate to verify the factor 1/a.
C \(e^{ax}+C\) This does not satisfy the stated relationship.
D \(\frac1x e^{ax}\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Integration · answered at 100 ms

07 Which response best completes this VCE-style item? The standard deviation of the sample mean is
A \(n/\sigma\) This does not satisfy the stated relationship.
B \(\sigma/n\) This does not satisfy the stated relationship.
C \(\sigma\sqrt n\) This does not satisfy the stated relationship.
D \(\sigma/\sqrt n\) This is the standard error of the mean.

Written for icaijy.com · U3–4 · Sample means · answered at 100 ms

08 Which response best completes this VCE-style item? A vector equation of a line is
A \(\vec r=\vec a\times\vec d\) This does not satisfy the stated relationship.
B \(\vec r=\vec a\cdot\vec d\) This does not satisfy the stated relationship.
C \(\vec r=\lambda\) This does not satisfy the stated relationship.
D \(\vec r=\vec a+\lambda\vec d\) A point plus a scalar multiple of a direction defines the line.

Written for icaijy.com · U3–4 · Vector lines · answered at 100 ms

09 A student is checking a worked solution. The sum of degrees in an undirected graph equals
A twice the number of edges Each edge contributes two degree incidences.
B the number of vertices This does not satisfy the stated relationship.
C twice the number of vertices This does not satisfy the stated relationship.
D the number of edges This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graph theory · answered at 100 ms

10 A student is checking a worked solution. A small p-value is evidence
A of zero sampling variation This does not satisfy the stated relationship.
B that the alternative has probability p This does not satisfy the stated relationship.
C that the null is certainly true This does not satisfy the stated relationship.
D against the null hypothesis It means the observed statistic is unusual under the null.

Written for icaijy.com · U3–4 · Hypothesis tests · answered at 100 ms

11 During a one-minute revision round: The number of ways to choose r objects from n without order is
A \(n!\) This does not satisfy the stated relationship.
B \(n^r\) This does not satisfy the stated relationship.
C \(n-r\) This does not satisfy the stated relationship.
D \(\binom nr\) Combinations ignore order.

Written for icaijy.com · U1–2 · Counting · answered at 100 ms

12 A student is checking a worked solution. If position is \(\vec r(t)\), acceleration is
A \(\int\vec r(t)dt\) This does not satisfy the stated relationship.
B \(|\vec r(t)|\) This does not satisfy the stated relationship.
C \(\vec r\prime(t)\) This does not satisfy the stated relationship.
D \(\vec r\prime\prime(t)\) Acceleration is the second time derivative of position.

Written for icaijy.com · U3–4 · Kinematics · answered at 100 ms

13 The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is
A \(ab-cd\) This does not satisfy the stated relationship.
B \(a+d\) This does not satisfy the stated relationship.
C \(ad-bc\) Use ad−bc.
D \(ac-bd\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Matrices · answered at 100 ms

14 During a one-minute revision round: The roots of \(z^n=1\) are equally spaced on the
A real axis This does not satisfy the stated relationship.
B parabola This does not satisfy the stated relationship.
C imaginary axis This does not satisfy the stated relationship.
D unit circle Their moduli are one and arguments differ by 2π/n.

Written for icaijy.com · U3–4 · Complex roots · answered at 100 ms

15 A student is checking a worked solution. The modulus of \(3+4i\) is
A 1 This does not satisfy the stated relationship.
B 7 This does not satisfy the stated relationship.
C 25 This does not satisfy the stated relationship.
D 5 Use the Pythagorean theorem.

Written for icaijy.com · U1–2 · Complex plane · answered at 100 ms

16 Which response best completes this VCE-style item? The negation of “all integers are positive” is
A no integers exist This does not satisfy the stated relationship.
B at least one integer is positive This does not satisfy the stated relationship.
C all integers are not positive This does not satisfy the stated relationship.
D at least one integer is not positive Negating a universal statement produces an existential counterexample.

Written for icaijy.com · U1–2 · Logic · answered at 100 ms

17 A student is checking a worked solution. A proof by contradiction begins by assuming
A a numerical example This does not satisfy the stated relationship.
B the negation of the desired conclusion A contradiction disproves the negation.
C the conclusion itself This does not satisfy the stated relationship.
D every lemma is false This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Proof · answered at 100 ms

18 Which response best completes this VCE-style item? The sum of degrees in an undirected graph equals
A twice the number of vertices This does not satisfy the stated relationship.
B the number of edges This does not satisfy the stated relationship.
C the number of vertices This does not satisfy the stated relationship.
D twice the number of edges Each edge contributes two degree incidences.

Written for icaijy.com · U1–2 · Graph theory · answered at 100 ms

19 A student is checking a worked solution. The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is
A \(a+d\) This does not satisfy the stated relationship.
B \(ac-bd\) This does not satisfy the stated relationship.
C \(ab-cd\) This does not satisfy the stated relationship.
D \(ad-bc\) Use ad−bc.

Written for icaijy.com · U1–2 · Matrices · answered at 100 ms

20 During a one-minute revision round: If position is \(\vec r(t)\), acceleration is
A \(|\vec r(t)|\) This does not satisfy the stated relationship.
B \(\vec r\prime\prime(t)\) Acceleration is the second time derivative of position.
C \(\vec r\prime(t)\) This does not satisfy the stated relationship.
D \(\int\vec r(t)dt\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Kinematics · answered at 100 ms

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